Motorized roller shades include a flexible shade fabric wound onto an elongated roller tube. The roller tube is rotatably supported so that a lower end of the shade fabric can be raised and lowered by rotating the roller tube. The roller tubes are generally in the shape of a right circular cylinder having various lengths for supporting shade fabrics of various width. Motorized roller shades include a drive system engaging the roller tube to provide for tube rotation.
For aesthetic reasons, it is desirable that the outer diameter of the roller tube be as small as possible. Roller tubes, however, are generally supported only at their ends and are otherwise unsupported throughout their length. Roller tubes, therefore, are susceptible to sagging if the cross-section of the roller tube does not provide for sufficient bending stiffness for a selected material. Therefore, increase in the length of a roller tube is generally accompanied by increase in the outer diameter of the tube.
In certain situations, such as for shading areas of very large width or for shading areas that are non-planar across their width, it may be desirable to use multiple roller shades. In these situations, it may also be necessary or desirable to use roller tubes having different lengths. Relatively long tubes might require that a larger diameter be used compared to shorter tubes in order to limit sagging.
Where multiple roller shades are used to shade a given area, the capability of raising or lowering the shades such that their lower ends move consonantly as a unit (i.e., simultaneously at the same speed) is desirable. However, two roller shades having tubes of differing diameter will not raise or lower a shade fabric at the same speed if they are rotated at the same rotational speed.
For any member that is rotated about a central axis, the linear speed at a surface of the rotating member will depend on the distance between the surface and the rotational axis. Thus, for a given rotational speed (i.e., rpm), the resulting linear speed (i.e., in/sec) at the outer surface of the tube will vary in direct proportion to outer tube diameter. Therefore, two roller tubes having differing outer diameters that are driven at the same rotational speed will have different linear speeds at the outer surface. The larger diameter tube will have a higher linear speed at the outer surface and, accordingly, will windingly receive, or release, the associated shade fabric at a faster rate than the smaller diameter tube.
The ability to provide consonant shade speed for two roller shades having tubes of differing diameters is further complicated because the shade speed for either one of the roller shades will not remain constant as the shade is raised or lowered between two shade positions. The winding receipt of a shade fabric onto a roller tube creates layers of overlapping material that increases the distance between the rotational axis and the point at which the shade fabric is windingly received compared to the distance at the tube outer surface. As a result, the shade speed will vary depending on the thickness of the overlapping layers of material received on the roller tube.